Séminaire Lotharingien de Combinatoire, B44c (2000), 3 pp.
Herbert S. Wilf
Identically Distributed Pairs of Partition Statistics
Abstract.
We show that many theorems which assert that two kinds of partitions of the
same integer n are equinumerous are actually special cases of a much
stronger form of equality. We show that in fact there correspond partition
statistics X and Y that have identical distribution functions. The
method is an extension of the principle of sieve-equivalence, and it yields
simple criteria under which we can infer this identity of distribution
functions.
Received: April 25, 2000; Accepted: May 19, 2000.
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